Add real TypeScript typecheck

[GHX5T-SOL]

Fixes #1

Summary:

• Replaces the syntax-only typecheck script with tsc --noEmit.
• Adds TypeScript and Node 22 typings, then removes the old local Node shim declarations.
• Wires the default npm test path through real typechecking before build/test execution.
• Updates tsconfig.json to ESNext/Bundler resolution so tsc checks the authored source imports while the existing build script continues rewriting runtime import specifiers.
• Fixes the strict type errors surfaced by the real compiler pass.

Validation:

• npm run typecheck
• npm test (131 tests)
• git diff --check HEAD~1 HEAD
• git show --format= --patch HEAD | gitleaks stdin --no-banner --redact --timeout 30

Notes:

• This does not add CI wiring; the issue notes that as later work.
• The build path is unchanged and still uses scripts/build.mjs.
• Prepared with AI assistance and verified locally.